Bound on Reheating Temperature with Dark Matter [Based on the work - - PowerPoint PPT Presentation

Bound on Reheating Temperature with Dark Matter

Ki -Young Choi

[Based on the work with Tomo Takahashi]

Contents

• 2. Dark matter in the early Matter Domination
• 1. Reheating temperature and early Matter Domination
• 3. Low bound on the reheating temperature
• 4. Discussion

Temperature of the Universe

What is the highest temperature? What is the lowest temperature? What is the available range of this initial high temperature?

Inflation: vacuum-dominated Oscillation : matter-dominated Decay : radiation-dominated Inflation and Matter-Domination

Reheating

During inflation, the Universe is cold. After inflation, the energy of the inflation is converted to the production of the light particles. Usually the inflaton field oscillates around vacuum and decay to produce light particles. The particles are thermalised and the Universe is heated to some

• temperature. We call the highest temperature when the radiation-

domination starts, reheating temperature. Early matter-domination (by inflaton) before reheating is inevitable.

H2 ⇠ ρ ⇠ a−3

Upper bound on Reheating Temperature

Energy scale of the inflation constrains the highest temperature of the reheating temperature.

V 1/4 ∼ ⇣ r 0.01 ⌘1/4 1016 GeV

ρ(Treh) < V

ρ(T) = π2 30g∗T 4

bound on tensor-to-scalar ratio

Treh < 1016 GeV

Energy during inflation

Early Matter-Domination and Reheating

Reheating and early matter-domination also happen in the scenarios of Moduli, curvaton, thermal inflation, axino, gravitino, .... When decoupled heavy particles are very weakly interacting, they decay very late in the early Universe. Temperature ~ MeV - GeV

H Treh ' ✓90 π2 ◆1/4p ΓMP

Reheating Temperature

[From Kolb & Turner]

ρ(T) = π2 30g∗T 4

Γ ' H T

H Treh ' ✓90 π2 ◆1/4p ΓMP

Matter-dom. Rad.-dom.

Low bound on Reheating Temperature

• 1. Big Bang Nucleosynthesis

: at low-reheating temperature, neutrinos are not fully thermalised and the light element abundances are changed,

as Treh & 0.5 − 0.7 MeV

• n the reheating temperatur
• r Treh & 2.5 MeV − 4 MeV

for hadronic decays [Kwasaki, Kohri, Sugiyama, 1999, 2000]

• 2. BBN+CMB+LSS

: precise calculation of the cosmic neutrino background and CMB

Treh & 4.7 MeV

[Salas, Lattanzi, Mangano, Miele, Pastor, Pisanti, 2015]

Local Thermal Equilibrium

• f protons and neutrons

Weak freeze-out Deuterium bottleneck

T 1 MeV

↔ (t 1 sec)

T ∼ 1 MeV (t ∼ 1 sec)

n p = e−(mn−mp)/T 1 6 n + p ↔ D + γ

T ∼ 0.07 MeV (t ∼ 3 min)

most neutrons to He4 small D, He3 Li7 Decay of free neutrons

n/p 1/7

n = g mT 2π 3/2 e−(m−µ)/T

mn − mp 1.29 MeV

n ↔ p + e− + ¯ νe n + νe ↔ p + e− p + ¯ νe ↔ n + e+

τn ' 880 sec

Big-Bang Nucleosynthesis

New bound on low-reheating temperature

• 3. Dark matter halos

: density perturbation during early matter-domination and no

• bservation of small scale DM halos.

[KYChoi, Tomo Takahashi, in preparation]

Treh & 30 MeV

Early Matter Domination and Reheating

[From Kolb & Turner]

ρ(T) = π2 30g∗T 4

Γ ' H T

H Treh ' ✓90 π2 ◆1/4p ΓMP

Early Matter-dom. Radiation-dom.

Evolution of Density Perturbation − δ ≡ δρ ρ

Inside horizon: Radiation (rel. particles) : oscillates decoupled DM (non rel. particles with vanishing pressure) : Rad-domination: logarithmically grows Matter-domination: linearly grows

− δ ≡ δρ ρ

scale factor horizon entry rad-matter equality Radiation domination Matter domination

1

non-linear growth

δ ∝ log a

δ ∝ a

∝ a

Evolution in the Standard Model

10−5

− δ ≡ δρ ρ

scale factor horizon entry rad-matter equality Radiation domination Matter domination

1

non-linear growth

δ ∝ log a

δ ∝ a

∝ a

Primordial Black Holes or UCMHs

10−5

If initially large

Primordial Black Holes or UCMHs

If primordial density perturbation is large:

δ & 0.1 The matters and radiation collapse when they enters the

horizon and make black holes (primordial black hole) No observation of primordial black hole rule out this large density perturbation.

δ & 10−3 It does not make black hole, but can make small scale

dm dominated halos (ultra compact mini halo, UCMH) No observation yet. The constraint depends on the properties of dark matter.

UCMHs in the Galaxy

• ⇧(r) ⇤

1 r 2.25

Observation of UCMHs with WIMP

WIMP dark matter Annihilation or decay of WIMPs in the UCMHs : gamma-ray, neutrino, cosmic rays. Fermi-LAT constrains strongly [Bringmann, Scott, Akrami, 2012]

f ≡ ΩUCMH/Ωm = β(R)fχ M 0

UCMH

Mi

UCMH Mass Fraction

UCMH mass fraction in the Milky Way

where fχ ≡ Ωχ/Ωm

with DM fraction

β(R) = 1 p 2πσχ,H(R) Z δmax

χ

δmin

χ

exp "

• δ2

χ

2σ2

χ,H(R)

# dδχ (

• probability of comoving size R can collapse to form UCMH

χ

M 0

UCMH

Mi .

• increase of the mass by grav. infall during MD

Mi ≃ 4π 3 ρχ(a)R3

phys

• R=1/(aH)

Probability to form UCMH

• CDM mass variance at horizon entry from power spectrum

σ2(R) = Z 1 W 2

TH(kR)Pδ(k)dk

k

: with minimum value of density contrast for UCMH at horizon entry

δmin

χ

(k, tk) =

[Bringmann, Scott, Akrami, 2013] It is roughly 0.001 at horizon entry in the standard Rad.-dom. Universe.

k (Mpc1) fmax M 0

UCMH (M) 108 107 106 105 104 103 102 101 1 10 102 103 104 105 106 107 108 109 1010 1011 1012 10 102 103 104 105 106 107 106 105 104 103 102 101 1

Galactic sources extragalactic sources Galactic diffuse

Constraints for UCMH with WIMP DM

We assume 100% annihilation of WIMPs into b¯ b pairs, a WIMP mass of mχ = 1 TeV and an effective annihi- lation cross-section of hσvi = 3 ⇥ 1026 cm3 s1. These

[Bringmann, Scott, Akrami, 2013]

❙ ❙

k (Mpc−1) Pδ(k)

WIMP kinetic decoupling

PR(k)

10−9 10−8 10−7 10−6 10−5 10−4 10−3 10−2 10−1 10−3 10−2 10−1 1 10 102 103 104 105 106 107 108 109 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 10−10 10−9 10−8 10−7 10−6 10−5 10−4 10−3 10−2

Allowed regions Ultracompact minihalos (gamma rays, Fermi-LAT) Ultracompact minihalos (reionisation, WMAP5 τe) Primordial black holes CMB, Lyman-α, LSS and other cosmological probes

Constraints on Primordial Power Spectrum

[Bringmann, Scott, Akrami, 2013]

Observation of UCMHs

UCMHs with non-WIMP dark matter : To observe by Gravitational effects only

• distortion in the macrolensed quasars

[Clark, Lewis, Scott, 2015] [Zackrisson 2013]

• pulsar timing
• astrometric microlensing

[Li, Erickcek, Law, 2012] Even with Smin feq & 0:009.

f . 0.1 f . 10−6

f ≡ ΩUCMH/Ωm = β(R)fχ M 0

UCMH

Mi

Constraints for UCMH by Pulsar Timing

[Clark, Lewis, Scott, 2015] Pulsar time can change when the UCMHs are moving across the line of sight. They obtain the bound on the fraction of UCMHs for different scales. This is constraint is gravitational, so universal. WIMP pulsar-timing

[Clark, Lewis, Scott, 2015]

Constraints on Power Spectrum by Pulsar Timing

UCMHS with early MD

Before reheating, the epoch matter-domination exists (early matter-domination). The perturbation which enters during early matter-domination can grow linearly and help to generate UCMHs. Non-observation of UCMHs can constrain the primordial power spectrum and the stage of early matter-domination.

− δ ≡ δρ ρ

scale factor horizon entry rad-matter equality Radiation domination Matter domination

1

UCMHs

δ ∝ log a

δ ∝ a

∝ a

UCMHs and early Matter-Domination

10−5

early matter domination reheating

Treh

To find δmin

χ

(k, tk) =

It is roughly 0.001 at horizon entry in the standard Radiation

• dominated Universe.

For early matter-domination, we need to make evolution from horizon entry to the deep inside until it forms the UCMHs. linear evolution collapse

c ðtcÞlin

• ðtcÞ

¼ 3 5 3 2 2=3 1:686:

time of collapse using linear theory The collapse should happen before some epoch, here we choose z = 1000, conservatively.

− δ ≡ δρ ρ

scale factor horizon entry rad-matter equality Radiation domination Matter domination

1

UCMHs

δ ∝ log a

δ ∝ a

∝ a

UCMHs and early MD

10−5

early matter domination reheating

Treh

f δmin

χ

δc =

δmax

χ

δσ = −2Φ0 − 2 3Φ0 ✓ k aiH(ai) ◆2 a ai ,

Growth of Density Perturbation

Density perturbation contrast of the dominating heavy particles

where δσ ≡ δρσ/ρσ,

During matter-domination epoch,

kreh = 0.011967 pc−1 ✓ Treh MeV ◆✓10.75 g∗s ◆1/3⇣ g∗ 10.75 ⌘1/2 . (3)

For decoupled dark matter, the evolution during early MD is same. Therefore at the time of reheating,

δχ ' 2 3Φ0 ✓ k kreh ◆2 for k < kdom,

δχ ' 2 3Φ0 ✓kdom kreh ◆2 for k > kdom.

The scale of reheating is

Decoupled Dark Matter: super-WIMP

k < kdom,

The scale of beginning early MD:

For WIMP dark matter, it is still in the thermal equilibrium during early MD and freeze-out. After decoupling, the density of WIMP grows even in the kinetic equilibrium

WIMP Dark Matter

δχ ' 5 4Φ0 ✓ k kreh ◆2 , [KYChoi, Gong, Shin, 2015] at reheating epoch

10-5 10-4 10-3 10-2 101 102 103 104 105 106 107 |δχ

min|

k (Mpc)-1 Treh=10 MeV, kdom/kreh=10 Treh=10 MeV, kdom/kreh=5 Treh=10 MeV, kdom/kreh=3

To form UCMSs with early MD

w/o early MD

e zc = 1000.

Bound on low-reheating Temperature

Fermi-LAT pulsar timing zc=1000

Treh & 30 MeV

[KYChoi, Tomo Takahashi, in preparation]

kdom/kreh Treh (MeV) 100 101 102 100 101 102 103 104

Treh & 500 MeV

Discussion

• 1. Reheating process follows the early matter-domination epoch.
• 2. Dark matter density perturbation growth during early

matter-domination before reheating and can generate large number of UCMHs.

• 3. Non-observation of UCMHs can constrain the low-reheating

temperature and gives new bound on the reheating temperature.